Numerical studies of dynamo action in a turbulent shear flow. I

We perform numerical experiments to study the shear dynamo problem where we look for the growth of a large-scale magnetic field due to non-helical stirring at small scales in a background linear shear flow in previously unexplored parameter regimes. We demonstrate the large-scale dynamo action in the limit where the fluid Reynolds number ($Re$) is below unity while the magnetic Reynolds number ($Rm$) is above unity; the exponential growth rate scales linearly with shear, which is consistent with earlier numerical works. The limit of low $Re$ is particularly interesting, as seeing the dynamo action in this limit would provide enough motivation for further theoretical investigations, which may focus attention on this analytically more tractable limit of $Re<1$ compared to the more formidable limit of $Re>1$. We also perform simulations in the regimes where (i) both ($Re$, $Rm$) < 1, and (ii) $Re>1$ and $Rm<1$, and compute all of the components of the turbulent transport coefficients (${\alpha }_{ij}$ and ${\eta }_{ij}$) using the test-field method. A reasonably good agreement is observed between our results and the results of earlier analytical works in similar parameter regimes.